As widely accepted as it is, the equality principle may be understood in, at least, three different ways. This paper, focused on the Inter-American context, examines firstly the problems of the standard conception of equality -i.e. as anti-discrimination-, showing that although it may solve specific problems, it cannot deal with the structural inequalities widely spread in Latin America. Secondly, we analyze the more ample scope offered by the conception of equality as antisubordination, in order to understand the deeply rooted causes of inequality in our social orders. Being these indentified, we add the more complex theoretical framework developed by N. Fraser, which accounts for both, redistribution and recognition issues when approaching inequalities. The wider scope on inequality provided by this theoretical framework improves not only our understanding of rights, but also expose the intimate connection between rights, deliberative democracy and equality, all three of them understood as the struggle for participatory parity of disadvantaged groups. As we believe it allows a better understanding of recent Inter-American Court of Human Rights decisions on indigenous peoples related cases, the last section of this paper is devoted to reinterpret these in order to test our thesis.